Stiff biological materials (SBMs), such as nacre and bone, are composites that display remarkable toughness enhancements over their primary constituents, which are brittle minerals. These enhancements are thought to be a consequence of different mechanisms made possible by the SBMs’ internal lamellar architecture. One such mechanism is the Cook–Gordon (crack-arrest-and-reinitiation) mechanism, whose operation manifests in flexural tests as a sawtooth pattern in the force–displacement curves. The curves from flexural tests carried out on marine sponge spicules, which also possess a lamellar architecture, also display a sawtooth-pattern, suggesting the presence of the Cook–Gordon mechanism. Intriguingly, the spicules were recently found not to display any significant toughness enhancement. To resolve this apparent contradiction, in the preceding paper (Kochiyama et al., 2021), we put forward the hypothesis that the sawtooth pattern was due to the spicules slipping at the tests’ supports. In this paper, we present a model for the spicule’s flexural tests in which we allow for the possibility for the specimen to slip at the test’s supports. We model contact between the specimen and the test’s supports using the Coulomb’s friction law. By choosing experimentally reasonable values for the friction coefficient, we were able to get the model’s predictions to match experimental measurements remarkably well. Additionally, on incorporating the spicules’ surface roughness into the model, which we did by varying the friction coefficient along the spicule’s length, its predictions can also be made to match the measured sawtooth patterns. We find that the sawtooth patterns in the model are due to slip type instabilities, which further reinforces the hypothesis put forward in our preceding paper.

硬质生物材料 (SBM)，例如珍珠层和骨骼，是一种复合材料，与其主要成分（脆性矿物）相比，其韧性显着增强。这些增强被认为是 SBM 的内部层状结构使不同机制成为可能的结果。其中一种机制是库克-戈登（Cook-Gordon）机制，其操作在弯曲测试中表现为力-位移曲线中的锯齿图案。对同样具有层状结构的海海绵针状体进行的弯曲测试的曲线也显示出锯齿状图案，表明存在 Cook-Gordon 机制。有趣的是，最近发现针状体没有显示出任何显着的韧性增强。为了解决这个明显的矛盾，在之前的论文（Kochiyama 等人，2021 年）中，我们提出了锯齿图案是由于针状体在测试支撑处滑动造成的假设。在本文中，我们提出了一个用于骨针弯曲测试的模型，其中我们考虑了试样在测试支撑处滑动的可能性。我们使用库仑摩擦定律对试样和测试支架之间的接触进行建模。通过为摩擦系数选择实验上合理的值，我们能够获得模型的预测以非常好地匹配实验测量值。此外，在将针状体的表面粗糙度纳入模型时，我们通过沿针状体长度改变摩擦系数来实现，其预测也可以与测量的锯齿图案相匹配。